\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t23\_e\_siec (TMNMByhH9sqpDP4ARcCQpSKHLS5p5fKwK4q)}
\maketitle
Let $ v2\_e\_siec : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_e\_siec : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_e\_siec : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_relat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_e\_siec : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_e\_siec : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_e\_siec : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_e\_siec : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_e\_siec : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_e\_siec : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_sysrel : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_partfun1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}((r1\_tarski~(k9\_xtuple\_0~\\
X1)~X0){\unicdbdjdcd}(k3\_relat\_1~(k4\_relat\_1~X0)~X1=X1))\end{array}
\label{hyp:ehfdbdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (v1\_relat\_1~X2){\unicdbdjdcd}((r1\_tarski~\\
X2~(k2\_zfmisc\_1~X0~X1)){\unicdbdjdcd}((r1\_tarski~(k9\_xtuple\_0~X2)~X0){\unicdcdcdhd}(r1\_tarski~\\
(k10\_xtuple\_0~X2)~X1)))\end{array}
\label{hyp:ehddpfdhjhdhchfgmg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_e\_siec~X0){\unicdcdcdhd}((v3\_e\_siec~X0){\unicdcdcdhd}(l1\_e\_siec~X0))){\unicdbdjdcd}\\
((r1\_tarski~(k10\_e\_siec~X0)~(k2\_zfmisc\_1~(k8\_e\_siec~X0)~(k7\_e\_siec~\\
X0))){\unicdcdcdhd}(r1\_tarski~(k11\_e\_siec~X0)~(k2\_zfmisc\_1~(k8\_e\_siec~X0)~\\
(k7\_e\_siec~X0))))\end{array}
\label{hyp:ehcdadpffgpfdhjgfgdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_e\_siec~X0){\unicdcdcdhd}((v3\_e\_siec~X0){\unicdcdcdhd}(l1\_e\_siec~X0))){\unicdbdjdcd}\\
((k10\_xtuple\_0~(u1\_e\_siec~X0)=k10\_xtuple\_0~(k1\_sysrel~(u1\_e\_siec~\\
X0))){\unicdcdcdhd}((k10\_xtuple\_0~(u1\_e\_siec~X0)=k9\_xtuple\_0~(k1\_sysrel~\\
(u1\_e\_siec~X0))){\unicdcdcdhd}((k10\_xtuple\_0~(u2\_e\_siec~X0)=k10\_xtuple\_0~\\
(k1\_sysrel~(u2\_e\_siec~X0))){\unicdcdcdhd}((k10\_xtuple\_0~(u2\_e\_siec~X0)=k9\_xtuple\_0~\\
(k1\_sysrel~(u2\_e\_siec~X0))){\unicdcdcdhd}(k10\_xtuple\_0~(u1\_e\_siec~X0)=k10\_xtuple\_0~\\
(u2\_e\_siec~X0))))))\end{array}
\label{hyp:ehbdddpffgpfdhjgfgdg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k6\_subset\_1}~{X0}}~{X1}}={{{k4\_xboole\_0}~{X0}}~{X1}}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k6\_partfun1}~{X0}}={{k4\_relat\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_e\_siec~X0){\unicdcdcdhd}((v3\_e\_siec~X0){\unicdcdcdhd}(l1\_e\_siec~X0))){\unicdbdjdcd}\\
(v1\_relat\_1~(k11\_e\_siec~X0))\end{array}
\label{hyp:egehpflgbdbdpffgpfdhjgfgdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_e\_siec~X0){\unicdcdcdhd}((v3\_e\_siec~X0){\unicdcdcdhd}(l1\_e\_siec~X0))){\unicdbdjdcd}\\
(v1\_relat\_1~(k10\_e\_siec~X0))\end{array}
\label{hyp:egehpflgbdadpffgpfdhjgfgdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_e\_siec~X0){\unicdcdcdhd}((v3\_e\_siec~X0){\unicdcdcdhd}(l1\_e\_siec~X0))){\unicdbdjdcd}\\
(k7\_e\_siec~X0=k10\_xtuple\_0~(u1\_e\_siec~X0))\end{array}
\label{hyp:egjdpffgpfdhjgfgdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_e\_siec~X0){\unicdcdcdhd}((v3\_e\_siec~X0){\unicdcdcdhd}(l1\_e\_siec~X0))){\unicdbdjdcd}\\
(k11\_e\_siec~X0=k4\_xboole\_0~(u2\_e\_siec~X0)~(k4\_relat\_1~(u1\_struct\_0~\\
X0)))\end{array}
\label{hyp:egbdddpffgpfdhjgfgdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_e\_siec~X0){\unicdcdcdhd}((v3\_e\_siec~X0){\unicdcdcdhd}(l1\_e\_siec~X0))){\unicdbdjdcd}\\
(k10\_e\_siec~X0=k4\_xboole\_0~(u1\_e\_siec~X0)~(k4\_relat\_1~(u1\_struct\_0~\\
X0)))\end{array}
\label{hyp:egbdcdpffgpfdhjgfgdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_e\_siec~X0){\unicdcdcdhd}((v3\_e\_siec~X0){\unicdcdcdhd}(l1\_e\_siec~X0))){\unicdbdjdcd}\\
(k8\_e\_siec~X0=k4\_xboole\_0~(u1\_struct\_0~X0)~(k7\_e\_siec~X0))\end{array}
\label{hyp:egbdadpffgpfdhjgfgdg}
\end{equation}
\begin{theorem}\label{thm:ehcdddpffgpfdhjgfgdg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_e\_siec~X0){\unicdcdcdhd}((v3\_e\_siec~X0){\unicdcdcdhd}(l1\_e\_siec~X0))){\unicdbdjdcd}\\
((k3\_relat\_1~(k4\_relat\_1~(k4\_xboole\_0~(u1\_struct\_0~X0)~(k10\_xtuple\_0~\\
(u2\_e\_siec~X0))))~(k4\_xboole\_0~(u2\_e\_siec~X0)~(k4\_relat\_1~(u1\_struct\_0~\\
X0)))=k4\_xboole\_0~(u2\_e\_siec~X0)~(k4\_relat\_1~(u1\_struct\_0~X0))){\unicdcdcdhd}\\
(k3\_relat\_1~(k4\_relat\_1~(k4\_xboole\_0~(u1\_struct\_0~X0)~(k10\_xtuple\_0~\\
(u1\_e\_siec~X0))))~(k4\_xboole\_0~(u1\_e\_siec~X0)~(k4\_relat\_1~(u1\_struct\_0~\\
X0)))=k4\_xboole\_0~(u1\_e\_siec~X0)~(k4\_relat\_1~(u1\_struct\_0~X0))))\end{array}$$
\end{theorem}
\end{document}
